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Most crop models consider ambient air temperature to drive various processes and rates, including heat stress effects. For example, APSIM (Keating et al., 2003) uses daily maximum temperatures, while modified CropSyst (Moriondo et al., 2011) considers mean temperatures between 8h00 and 14h00 and SIMPLACE’s heat stress module (Rezaei et al., 2013) uses a daily average weighted four times more heavily to the daily maximum than the minimum temperature. However, heat stress impacts on grain set in a crop stand are likely determined by tissue or canopy temperature (Jagadish et al., 2007; Craufurd et al., 2013; Siebert et al., 2014; van Oort et al., 2014), which can differ substantially from air temperature (Siebert et al., 2014) depending on crop transpiration rates, ambient CO2 concentrations and soil water status (Ferrise et al., 2011). Across more than 20
irrigated cultivars of spring wheat in a very hot environment with all mean monthly maximum temperatures above 30 °C, Amani et al. (1996) found a strong negative correlation between canopy temperature depression beneath the ambient air temperature and grain yield. While the authors do not attribute this to heat stress, the results provide a compelling evidence for the consideration of canopy temperature and not air temperature when crop models do not consider mechanistic representations of stomatal conductance and photosynthesis, particularly under water limiting conditions. Likewise in wheat, Idso et al. (1977) established a strong negative relationship between canopy temperature depression (beneath air temperature), at constant vapour pressure deficit and incident radiation (Idso et al., 1981a; Idso et al., 1981b; Jackson et al., 1981), resulting from different levels of water stress.
Simulation of canopy temperature is generally difficult as it is a complex function of standard meteorological parameters in addition to canopy resistance to water flow and aerodynamic resistance to heat and vapour transfer (Monteith and Unsworth, 1990). Furthermore, canopy temperature measured with an infrared thermometer is distinct from aerodynamic temperatures at the level of the surface, particularly for sparse canopies (Stewart et al., 1994; Lhomme et al., 2000; Colaizzi et al., 2004; Matsushima, 2005; Mihailovic and Eitzinger, 2007; Boulet et al., 2012) due to variations of emissivity with time of day (Colaizzi et al., 2004) or viewing angle (Huband and Monteith, 1986). Physically robust expressions for surface and aerodynamic canopy temperatures, such as that of Mihailovic and Eitzinger (2007), require extensive parameterization for stability functions (Paulson, 1970; Monteith and Unsworth, 1990) commonly defined in terms of the Richardson number or Monin-Obuhkov length (Monteith and Unsworth, 1990) making their use for crop models applied at the field and larger scales problematic. However, in a comparison of
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eight methods for estimating aerodynamic resistance and associated stability functions for maize, Liu et al. (2007) found that some of the simpler, more empirical methods performed as well as more complex ones using the Monin-Obuhkov length.
A simplified expression for canopy temperature is derived from a daily canopy energy balance by equating net radiation to latent and sensible heat fluxes, assuming the soil heat flux is negligible and ignoring the stability correction factors in the aerodynamic resistance terms (Idso et al., 1981a; Jackson et al., 1981; Clawson et al., 1989). While assumptions about neutral stability conditions, employed in formulations of reference evapotranspiration from well watered cropped grass surfaces (Allen et al., 1998; Allen et al., 2005) lead to greatly simplified expressions for canopy temperature, Tc, they are likely not valid under conditions when transpiration is reduced. In addition to the error introduced by assuming neutral stability conditions, and the challenges of having good quality data common to estimating reference evapotranspiration (Allen et al., 1998) two other issues present challenges for its implementation in field and larger scale crop models. Firstly, all meteorological variables should be measured over the crop being studied (Idso et al., 1977). While this is seldom strictly observed for calculation of reference evapotranspiration (Allen et al., 1998), significant deviation is expected in wind speeds over different crops, though methods are available to translate wind speeds measured over one crop to another (Allen and Wright, 1997). Finally, specification of the canopy resistance term is expected to be very difficult in conditions where crops experience water stress or stomatal conductance is reduced. As a simplification to avoid the latter challenge, Clawson et al. (1989) estimate the canopy temperature lower and upper limits with assumptions about stomatal conductance at full and no transpiration, respectively (Idso et al., 1981a; Jackson et al., 1981; Clawson et al., 1989). Actual canopy temperature will lie between these limits, and depend on the transpiration rate. On a daily basis this could be estimated as the ratio of actual crop transpiration to potential crop transpiration, though water stress and canopy temperatures vary throughout the day, and average daily water stress is likely to underestimate heat stress effects. Further, errors introduced using erroneous estimates of aerodynamic resistance, which is a function of wind speed, would need to be evaluated, as it has a strong influence on the upper and lower temperature limits. However, in the review of Liu et al. (2007), the error associated with wind speed and assumptions related to the roughness lengths of momentum and heat were larger than those associated with method of estimating aerodynamic resistance.
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Much simpler and empirical examples of representing canopy temperature exist. In a model of heat stress effects on rice sterility, van Oort et al. (2014) use an empirical expression of diurnal daily temperatures and relative humidity to estimate panicle temperature. The SIRIUS wheat simulation model (Jamieson et al., 1998) uses canopy temperature (Jamieson et al., 1995), calculated from a canopy level energy balance assuming neutral stability conditions, and no surface resistance term as latent heat flux is estimated from Penman (1948) which uses an empirical wind function (Jensen et al., 1990). Simulations of anthesis dates and final yield under different sowing dates improved when canopy temperature was used (Jamieson et al., 1995), though the impacts of heat stress were not investigated. In STICS (Brisson et al., 2003), a simple empirical formulation of canopy temperature varies with average temperature, net radiation, actual transpiration and soil evaporation fluxes, and the aerodynamic resistance, computed from Shuttleworth and Wallace (1985). Though fairly simple and making assumptions of neutral stability, the expression allows to calculate canopy temperature for conditions of variable LAI which control the contribution of soil sensible and latent energy fluxes (Shuttleworth and Wallace, 1985; Shuttleworth and Gurney, 1990).
It may be possible to avoid a direct calculation of canopy temperature, when water stress occurs frequently by directly simulating the negative effects of water stress on grain number. For example, Lobell et al. (2013) found maize grain number decrease with increasing temperature was adequately simulated with APSIM and attributed the response to increased vapour pressure deficit with higher temperatures leading to increased water stress. In APSIM-Maize, water stress reduces the grain number by reducing the grain demand for carbohydrates, in the same period as the high temperature stress factor on grain number. Such a response is consistent with that due to increased leaf temperatures resulting from reduced transpiration, as well as the delay in silking and lower rates of silk elongation that occur when maize is subjected to water deficit at flowering (Herrero and Johnson, 1981). However, such approaches do not aid in determining heat stress effects in fully transpiring crops. The interactions of high temperature and water stress contained in APSIM- Maize should likely only be implemented when the canopy temperature (air temperature in APSIM and most crop systems models) is at or close to the crop’s critical temperature for high temperature stress on grain number. APSIM applies this stress factor for all air temperature and crop sensitivity combinations suggesting they are estimating the impacts water stress only, and not elevated canopy temperature effects.
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